I have an apartment in Arlington, VA and the black population of Washington, D.C is about 90 percent of the population. While your conclusion that there are more blacks in the USG workforce, that may be true at my VA Hospital in Fayetteville NC where some offices with black supervisors have not hired anyone other than blacks in over 22 years; family ties are strong and nepotism runs deeper at that VA.
I think national black population is around 13%.
Gov’t offices in DC are much more than 13% blacks.